Following... I have the same problem after swapping my 2004 Mazda3 2.3 with a 2.5. No go in R or D. Drained fluid and replaced TC seal in tranny while the trans was out. Re-filled with 4 quarts, fluid is past full on dipstick, but i'm sure when it fills the TC and lines, it will need more. I seated the TC in the trans / pump before bolting up to the engine and flywheel. Also, used the stock 2.3 flywheel.
I have checked the connections to the trans. All are plugged in.
When in drive, and rev the engine a little the gear numbers will change from 1 to 2 to 3, like it is trying to shift due to the input shaft speed.

I figured out my issue. I used the wrong flexplate. Must have gotten the two mixed up somehow. The 2004 flexplate is different. You'll need to use the 2004 flex plate and Torque Converter. The thicknesses of the TC are different. So in my case, the torque converter is not reaching the trans oil pump becuase the flex plate pulled it toward the engine by about an half inch.
Make sure you put the TC into the trans before installing the trans. You need to turn the TC while lightly pushing toward the trans to get it to slip into place. There are two flat spots on the end that line up with the trans fluid pump. You'll fill it when it slips in. Then mate the engine up with the trans and bolt up the TC to the flex plate through the starter hole. Make sure there is not gap between the TC and flex plate when they mate, before you tighten the nuts to the TC.

Fredster, a good way to confirm that the fitment is off is when you matted the trans to the engine, you shouldn't be able to fully mate the two until the torque converter bolts are aligned into the flexplate holes. The flex plate shoudl be firmly pressing against the torque converter, but not interfearing with mating the trans to engine.
Since you already have it together and I imagine the trans oil pump is not engaged, you can pull the started to access the TC nuts, remove all 4 nuts. Wedge some dense foam or tapered sticks in between the TC and Flexplate to apply light pressue (you'll need to have the pressue balanced), then spin the crankshaft with a 21mm socket on the front crank bolt. once the TC lines up with the trans fluid pump, it will slide into place making a gap between the TC and flexplace.
Short story is, pull the trans and swap the flex plate and TC back to the 2004 original.
I just had to do that with mine last night. I knew I had to use the 2004 flexplate, but inadvertantly got the two mixed up and grabbed the wrong one. I can't tell you how hard I was kicking my own ass last night. 5 hours waisted becuase I didn't take the 5 minutes to validate I grabbed the wright flexplate.
When installing the TC to the trans, support the center nipple on the TC and slowly spin it. It will line up with the splins for the trans input shaft pretty quick and easy. Then you need to keep doing this until it slides in about another inch. You'll feal it pop into place when it lines up with the pump. You don't need to push hard, just light pressure toward the trans. I did this and then while installing the trans, the TC popped out slightly and got miss aligned with the pump. I knew this when there was pressure the last half inch of trying to get the trans bolted to the engine. I had to tighten the mating bolts just enough to apply pressure to the TC and flexplate then spun the engine over with a socket on the front. After spining it nearly a full revolution, it popped into place, again. Then I could tighten the mating bolts all the way and the engine would still spin freely. If you bolt the engine and trans together without the TC being aligned with the pump, the flexplate will bind and it will be very hard to turn the crankshaft with a socket and driver.
I hope this is helpful to you.

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